Question

Describe galvanic cells that use the following reactions. In each case, write the anode and cathode half-reactions and sketch the experimental setup. Label the anode and cathode, identify the sign of each electrode, and indicate the direction of electron and ion flow. (a) \(3 \mathrm{Cu}^{2+}(a q)+2 \operatorname{Cr}(s) \longrightarrow 3 \mathrm{Cu}(s)+2 \mathrm{Cr}^{3+}(a q)\) (b) \(\mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g)\) (c) \(\mathrm{Cl}_{2}(g)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}^{4+}(a q)+2 \mathrm{Cl}(a q)\)

Short answer

Each reaction requires a setup with a distinct anode and cathode, electron flow from anode to cathode, and ion flow through a salt bridge for charge balance.

Step-by-step solution

Balance the Reaction

Each given reaction must be balanced for the number of atoms and charges. Here they are already balanced as given in the exercise.

Identify Anode and Cathode for Reaction (a)

For the reaction \(3 \mathrm{Cu}^{2+}(aq) + 2 \operatorname{Cr}(s) \rightarrow 3 \mathrm{Cu}(s) + 2 \mathrm{Cr}^{3+}(aq)\), \(\operatorname{Cr}(s)\) is oxidized to \(\mathrm{Cr}^{3+}(aq)\), making it the anode where oxidation occurs. \(\mathrm{Cu}^{2+}(aq)\) is reduced to \(\mathrm{Cu}(s)\), making it the cathode where reduction occurs.

Write the Half-reactions for Reaction (a)

Anode (oxidation): \(\operatorname{Cr}(s) \rightarrow \mathrm{Cr}^{3+}(aq) + 3e^-\). Cathode (reduction): \(\mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s)\).

Sketch the Experimental Setup for Reaction (a)

Draw two beakers connected by a salt bridge. The anode (\(\operatorname{Cr}(s)\)) is marked negative and the cathode (\(\mathrm{Cu}(s)\)) is marked positive. Electrons flow from anode to cathode through the external circuit. Ions flow through the salt bridge to maintain charge balance.

Identify Anode and Cathode for Reaction (b)

For the reaction \(\mathrm{Pb}(s)+2 \mathrm{H}^{+}(aq) \rightarrow \mathrm{Pb}^{2+}(aq)+\mathrm{H}_2(g)\), \(\mathrm{Pb}(s)\) is oxidized to \(\mathrm{Pb}^{2+}(aq)\), so \(\mathrm{Pb}(s)\) is the anode. \(\mathrm{H}^{+}(aq)\) is reduced to \(\mathrm{H}_2(g)\), making it the cathode.

Write the Half-reactions for Reaction (b)

Anode (oxidation): \(\mathrm{Pb}(s) \rightarrow \mathrm{Pb}^{2+}(aq) + 2e^-\). Cathode (reduction): \(2 \mathrm{H}^{+}(aq) + 2e^- \rightarrow \mathrm{H}_2(g)\).

Sketch the Experimental Setup for Reaction (b)

Draw two beakers connected by a salt bridge. The anode (\(\mathrm{Pb}(s)\)) is marked negative and the cathode (where \(\mathrm{H}_2\) is produced) is marked positive. Electrons flow from the anode to the cathode. Ions flow through the salt bridge to maintain charge neutrality.

Identify Anode and Cathode for Reaction (c)

For the reaction \(\mathrm{Cl}_2(g) + \mathrm{Sn}^{2+}(aq) \rightarrow \mathrm{Sn}^{4+}(aq) + 2 \mathrm{Cl}^-(aq)\), \(\mathrm{Sn}^{2+}(aq)\) is oxidized to \(\mathrm{Sn}^{4+}(aq)\), so it is the anode. \(\mathrm{Cl}_2(g)\) is reduced to \(\mathrm{Cl}^-(aq)\), making it the cathode.

Write the Half-reactions for Reaction (c)

Anode (oxidation): \(\mathrm{Sn}^{2+}(aq) \rightarrow \mathrm{Sn}^{4+}(aq) + 2e^-\). Cathode (reduction): \(\mathrm{Cl}_2(g) + 2e^- \rightarrow 2 \mathrm{Cl}^-(aq)\).

Sketch the Experimental Setup for Reaction (c)

Draw two containers connected by a salt bridge. The anode, containing \(\mathrm{Sn}^{2+}\), is marked negative and the cathode, where \(\mathrm{Cl}_2\) gas is introduced, is marked positive. Electrons flow from the anode to the cathode and ions flow through the salt bridge to maintain electrical neutrality.

Key concepts

Electrochemical Reactions

Electrochemical reactions are processes where chemical energy is converted into electrical energy or vice versa. These reactions take place in electrochemical cells, which can either be galvanic or electrolytic. In a galvanic cell, a spontaneous redox reaction generates an electric current that can be harnessed to do work. This process involves the transfer of electrons from one species to another, where oxidation occurs at one electrode, and reduction occurs at the other. To better understand these reactions, it is crucial to examine the role of the anode and cathode as well as how half-reactions contribute to the overall process.

Anode and Cathode Identification

In every galvanic cell, there are two primary components: the anode and the cathode. Identifying which is which is integral to understanding the cell's operation.

• Anode: This is the site where oxidation occurs. Electrons are released from the substance at the anode, marking this electrode as negative in charge within a galvanic cell. For example, in the reaction between copper and chromium, chromium ( \( \text{Cr}(s) \)) serves as the anode, as it is oxidized to \( \text{Cr}^{3+}(aq) \).
• Cathode: This is where reduction takes place. Electrons enter a substance at the cathode, which is positive in a galvanic cell. In the same example, copper ions ( \( \text{Cu}^{2+}(aq) \)) are reduced to copper metal ( \( \text{Cu}(s) \)), making this the cathode.

Always ensure to distinctly label these electrodes to correctly understand the electron flow and roles within the cell.

Half-Reactions

A half-reaction demonstrates either the oxidation or reduction process of a redox reaction, split into its separate components. This division helps in balancing the number of electrons transferred in a full reaction.

• Oxidation Half-Reaction: Represents the loss of electrons. An example would be the chromium solid ( \( \text{Cr}(s) \)) being oxidized to chromium ion ( \( \text{Cr}^{3+}(aq) \)): \[ \text{Cr}(s) \rightarrow \text{Cr}^{3+}(aq) + 3e^- \].
• Reduction Half-Reaction: Displays the gain of electrons. For instance, the transformation of copper ions ( \( \text{Cu}^{2+}(aq) \)) to copper solid ( \( \text{Cu}(s) \)): \[ \text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s) \].

Breaking the reaction into half-reactions is vital for analyzing and designing electrochemical cells.

Electron Flow in Cells

Understanding electron flow in galvanic cells is key to grasping how these cells function.

• Electrons always flow from the anode to the cathode through the external circuit. This movement provides the current that can do electrical work, such as lighting a bulb or powering a device.
• In the copper-chromium cell, electrons are released from the oxidation of chromium at the anode and travel through the wire to the cathode, where they are consumed in the reduction of copper ions.
• Ions in the solution flow through a salt bridge to balance the charge between the two solutions, allowing the process to continue in equilibrium.

Keeping these principles in mind ensures the proper interpretation and application of galvanic cells in various contexts.